Maximum Likelihood Recursive State Estimation using the Expectation Maximization Algorithm

TL;DR

This paper introduces a recursive state estimation method for complex models using particle filters combined with the Expectation Maximization algorithm, providing a practical approach for maximum likelihood estimation in challenging scenarios.

Contribution

It presents a novel recursive estimation framework that integrates particle filtering with EM for non-linear, non-Gaussian models, including convergence analysis and reinitialization strategies.

Findings

Algorithms effectively estimate MLE in multimodal, truncated, and skewed densities.

Convergence properties are proven and demonstrated through examples.

Reinitialization enables convergence in complex density scenarios.

Abstract

A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute the maximum likelihood state estimate iteratively. Algorithms for maximum likelihood state filtering, prediction and smoothing are presented. The convergence properties of these algorithms, which are inherited from the Expectation Maximization algorithm, are proven and examined in two examples. It is shown that, with randomized reinitialization, which is feasible because of the algorithm simplicity, these methods are able to converge to the Maximum Likelihood Estimate (MLE) of multimodal, truncated and skewed densities, as well as those of disjoint support.